List any restrictions on the domain for the equation [tex] \frac{x+9}{x+2} [/tex]

Answer:

x = -2/3; x = 5/2.

Step-by-step explanation:

6x 2 - 11x - 10 = 0

Use the 'ac' method:

6 * -10 = -60. We need 2 numbers whose product is -60 and whose sum is -11.

That would be -15 and +4.  So we write:

6x^2 - 15x + 4x - 10 = 0      Factor by grouping:

3x(2x - 5) + 2(2x - 5) = 0

(3x + 2)(2x - 5) = 0

x = -2/3; x = 5/2.

to convert feet to miles you would use a ratio of feet over miles

 so the answer would be B

The distance it will take a car traveling at 45 mph to stop on dry, level concrete is 171 feet. If an accident occurs 200 feet ahead, one can travel at a maximum speed of approximately 58.4 mph to avoid the accident. The answers were calculated using the given equation for stopping distance and the speed of the car.

To address this question, we first need to make use of the equation d(v)=1.1v+0.06v²

First, let's answer part a): to find how many feet it will take a car traveling at 45 mph to stop, we simply substitute v with 45 in the equation, resulting in d = 1.1(45) + 0.06(45)² = 49.5 + 121.5 = 171 feet.

For part b), we need to solve the equation for v when d is equal to 200 feet. This is a quadratic equation (1.1v + 0.06v^2 = 200) and can be solved using the quadratic formula, or a method such as factoring or completing the square. Using the quadratic formula, we find that v ≈ 58.4 mph.

Therefore, if an accident happens 200 feet ahead, the maximum speed at which one can travel to avoid being involved in the accident is approximately 58.4 mph.

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a) At 45 mph, stopping distance is 171 feet. b) To avoid a 200-ft accident, max speed is 48.33 mph.

a) To find the stopping distance when the car is traveling at 45 mph, substitute v = 45 into the equation:

d(45) = 1.1(45) + 0.06(45)^2

= 49.5 + 121.5

= 171 feet

b) To find the maximum speed to avoid a 200 feet accident, set d(v) = 200 and solve for v:

1.1v + 0.06v^2 = 200

0.06v^2 + 1.1v - 200 = 0

Using the quadratic formula:

v = [-b ± √(b^2 - 4ac)] / (2a)

v = [-1.1 ± √(1.1^2 - 4(0.06)(-200))] / (2 * 0.06)

v ≈ [-1.1 ± √(1.21 + 48)] / 0.12

v ≈ [-1.1 ± √49.21] / 0.12

Now, solve for v:

v ≈ [-1.1 ± 7] / 0.12

This gives two solutions:

v ≈ (-1.1 + 7) / 0.12 ≈ 48.33 mph (Approx.)

v ≈ (-1.1 - 7) / 0.12 ≈ -63.33 mph (Not applicable)

Therefore, the maximum speed to avoid the accident is approximately 48.33 mph.

The simplification of 1/4 (-12+4/3) first involves simplifying the operation in the parentheses which gives -10.67. Multiplying this by 1/4 we get -2.67.

To simplify the expression 1/4 (-12+4/3), first simplify the operation in the parentheses.

-12 + 4/3 equals -12 + 1.33 (approx.), which simplifies to -10.67.

Then, multiply this result by 1/4. So, 1/4 of -10.67 equals -2.67 (approx.).

So, 1/4 (-12+4/3) simplifies to -2.67.

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Thomas = x

Julian = x-10

x +x-10 = 74

2x-10 = 74

2x = 84

x = 84/2 = 42

Thomas is 42

Julian is 32

Transformations of the functions include a vertical shift, reflection and vertical shift, and a horizontal and vertical shift for three different pairs respectively. Specific (x, y) data pairs demonstrate these transformations on the graphs.

We have three functions, f(x) and g(x), and we will describe the transformation from f(x) to g(x) for each:

The transformations can be sketched by plotting specific (x, y) data pairs and shifting the graphs accordingly.

multiply 152 by 15%

152 * 0.15 = 22.80 ( amount of discount

152 - 22.80 = 129.20 ( sale price)

By setting up a system of equations based on the total number of sweets sold and the total amount of money made, we find that Tiffany and Adele sold 11 cookies and 14 brownies.

To determine how many cookies and brownies Tiffany and Adele sold, we can set up a system of equations. Let's define the number of cookies sold as x and the number of brownies sold as y.

The first equation comes from the total number of sweets sold: x + y = 25. The second equation is based on the total amount of money made: 1*x + 1.50*y = 32.

Solving this system of equations will give us the number of each type of sweet sold.

To solve the system of equations, we can use substitution or elimination. I'll use substitution:

Tiffany and Adele sold 11 cookies and 14 brownies.

Answer:

-16         81       19

Step-by-step explanation:

Answer: A

Step-by-step explanation:

Using implicit differentiation, it is found that the rate of change of an edge is of -0.0533 meters per minute.

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The volume of a cube of edge e is given by:

[tex]V = e^3[/tex]

In this problem, the volume is of 125 m³, thus, we solve the above equation to find the length of an edge, in metres.

[tex]V = e^3[/tex]

[tex]125 = e^3[/tex]

[tex]e = \sqrt[3]{125}[/tex]

[tex]e = 5[/tex]

Now, for the rate of change, we need to apply the implicit differentiation, thus:

[tex]V = e^3[/tex]

[tex]\frac{dV}{dt} = 3e^2\frac{de}{dt}[/tex]

[tex]\frac{dV}{dt} = 3(5)^2\frac{de}{dt}[/tex]

[tex]\frac{dV}{dt} = 75\frac{de}{dt}[/tex]

Volume decreases at a rate of 4 cubic meters per minute, thus:

[tex]\frac{dV}{dt} = -4[/tex]

The rate of change of an edge is [tex]\frac{de}{dt}[/tex]. Then:

[tex]-4 = 75\frac{de}{dt}[/tex]

[tex]\frac{de}{dt} = -\frac{4}{75}[/tex]

[tex]\frac{de}{dt} = -0.0533[/tex]

The rate of change is of -0.0533 cubic meters per minute.

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A compound statement can be represented in symbolic logic as p ∧ q

The statement "A piece of paper is an object that can be drawn on" is not a compound statement

Reason:

The given statement is "A piece of paper is an object that can be drawn on"

The given statement is made up of just one subject which is 'a piece of paper'. The statement also has just one predicate, which is 'is an object that can be drawn on'

Therefore;

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To calculate the perimeter of the rectangular sandbox, use the formula P = 2l + 2w, where l is the length and w is the width. For the given dimensions, 31.7 meters in length and 24.5 meters in width, the perimeter is 112.4 meters.

The question asks us to calculate the perimeter of a rectangular sandbox. The formula to calculate the perimeter of a rectangle is 2 times the length plus 2 times the width, often written as P = 2l + 2w.

Given the dimensions of the sandbox, the length (l) is 31.7 meters, and the width (w) is 24.5 meters.

We calculate the perimeter as follows:

Therefore, the perimeter of the rectangular sandbox is 112.4 meters.

Answer:

its a

Step-by-step explanation:

Answer:

19 1/2 ft

Step-by-step explanation:

hope this helped

A wheel turn 60π radians per second.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

A wheel turns 1,800 revolutions per minute.

Now,

Since, A wheel turns 1,800 revolutions per minute.

Hence, Number of revolution in one seconds = 1800 / 60

                                                                       = 30

We know that;

⇒ 1 revolution = 2π radian

So, Number of revolution in radian per second = 30 × 2π

                                                                         = 60π

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The solid lying above the cone z = x^2 + y^2 and below the sphere x^2 + y^2 + z^2 = z, in spherical coordinates, is described by the inequalities 0 ≤ ρ ≤ 2 cos φ (W.r.t the sphere) and φ ≥ π/4 (W.r.t the cone), with 0 ≤ θ ≤ 2π (full revolution for θ).

In spherical coordinates, we represent a point in space using three values: ρ (the distance from the origin), φ (the angle measured from the positive z-axis down to the line connecting the origin and the point), and θ (the angle measured in the x-y plane from the positive x-axis to the projection of the line segment from the origin to the point).

The given cone z = x2 + y2 in spherical coordinates becomes ρ cos φ = ρ2 sin2 φ, which simplifies to tan φ = 1/ρ or φ = π/4. This is because for a cone with vertex at the origin, φ is constant. So, our first inequality is φ ≥ π/4.

The sphere's equation x2 + y2 + z2 = z becomes ρ2 = ρ cos φ, which further simplifies to ρ = 2 cos φ. So, the second inequality is ρ ≤ 2 cos φ, which bounds ρ from above by the sphere.

In summary, the solid is described by the inequalities 0 ≤ ρ ≤ 2 cos φ and φ ≥ π/4, with 0 ≤ θ ≤ 2π (since θ revolves full circle in spherical coordinates).

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The solid can be described using the inequalities: 0 ≤ r ≤ cos(θ), 0 ≤ θ ≤ 2π, and 0 ≤ ϕ ≤ π. These inequalities define the limits for the radius, polar angle, and azimuthal angle in spherical coordinates.

To describe the solid in terms of inequalities involving spherical coordinates, we need to find the limits for the radius, polar angle, and azimuthal angle.

Considering the given information, the solid lies above the cone z = x2 + y2, which implies that the z-coordinate ranges from 0 to r2.

As for the sphere x2 + y2 + z2 = z, we can rewrite it in spherical coordinates as r2 = r cos(θ) or r = cos(θ).

Therefore, the solid can be described using the following inequalities in spherical coordinates:

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